A communication system is formed, at a minimum, of a sending station and a receiving station, interconnected by a communication channel. Data that is to be communicated between the sending and the receiving stations is converted, by the sending station, into a form to permit its communication upon the communication channel. And, the receiving station operates to recover the informational content of the data, representations of which are detected at the receiving station.
Many varied types of communication systems have been developed and deployed to permit effectuation of many types of communication services. As technological advancements permit, improvements to existing such communication systems are made, and new types of communication systems are developed and deployed.
Amongst the technological advancements that have been implemented in communication systems have been advancements in digital communication techniques. Digital communication techniques, when implemented in a communication system, provide the capability of the communication system more efficiently to utilize the communication resources allocated thereto. By increasing the efficiency by which the communication resources of the communication system are utilized, the communication capacity of the communication system is increased. For instance, the bandwidths of the communication channel extending between the sending and receiving stations of a communication system are sometimes of limited allocations. That is to say, the communication capacity of such a communication system is constrained by the bandwidth available upon the communication channel upon which to communicate data.
A radio communication system is an exemplary type of communication system. In a radio communication system, the communication channel that extends between the sending and receiving station is defined upon a radio link, i.e., a portion of the electromagnetic spectrum. Because data is communicated on radio channels, the need to utilize a wireline, conventionally required in a wireline communication system, upon which to define channels is obviated. Radio communication systems permit for the effectuation of communication services when formation of a wireline connection between the sending and receiving stations is inconvenient or impractical. Additionally, a radio communication system is implementable as a mobile communication system in which one, or both, of the sending and receiving stations is permitted mobility.
A cellular communication system is a type of radio communication system that forms a mobile communication system. In a cellular communication system, mobile stations communicate by way of radio channels defined upon a radio air interface with network based communication stations. Telephonic communication of data, both of voice and of non-voice data, is effectuable pursuant to conventional cellular communication systems. With the implementation of digital communication techniques in cellular communication systems, data-intensive communication services are effectuable.
To facilitate communication of data in such digital cellular communication systems, as well as in other digital communications, data coding schemes have been devised. For instance, channel encoders are regularly utilized that assign symbols to binary representations of data that is to be communicated pursuant to the communication service. Corresponding channel decoders operate in reverse manners to convert detected symbol values into binary form. In some existing cellular communication systems, for instance, QPSK (quadrature phase shift keying) modulation is utilized in which symbols are assigned during channel encoding and modulation operations in which symbols are selected from an allowable, QPSK symbol set. Each symbol is defined in terms of an I-component and a Q-component. The QPSK scheme is a two-dimensional scheme. Other two-dimensional schemes are known and used in some other communication systems. By extension, three dimensional and higher dimensional schemes are also known and are amenable for implementation to facilitate effectuation of communication of data pursuant to a communication service.
Communications devices, such as sending stations and receiving stations, of a digital communication system, are sometimes required to carry out computationally intensive operations. The need to carry out the computationally intensive operations limits the speed at which the communication operations can be carried out and requires complex, and therefore relatively costly circuitry, to carry out such operations. For instance, the operations that are sometimes required to be carried out upon the data include the calculation of Euclidean norms. Calculation of Euclidean norms requires both squaring and square root operations. Euclidean norm calculations are required to be formed, for instance, at modem devices that form parts of the communication stations of a cellular communication system. A modem forming part of a communication device, e.g., of a CDMA based (code-division, multiple-access-based) cellular communication system, must perform Euclidean norm operations pursuant to operations of its various functions, such as searching, dll, transmitting, etc. functions.
Calculating the Euclidean norms in a two dimensional scheme is difficult, particularly when such operations are required to be performed quickly and successively upon successive data symbols of data that is communicated to effectuate a communication service. Calculation of Euclidean norms in higher dimensional schemes become prohibitively complex, particularly at high data rates.
Approximation techniques by which to approximate Euclidean norms are therefore sometimes used in existing systems and proposed for systems that shall utilize multidimensional techniques. Approximation techniques are also sometimes used in systems that utilize two-dimensional techniques. To be effective, any approximation technique must be accurate while also being of reduced computational complexity. While various approximation techniques are known to approximate two dimensional Euclidean norms, their application to higher dimensional Euclidean norm approximations also becomes computationally complex. As approximation techniques are presently not generally available for approximating quickly and accurately higher dimensional Euclidean norms, modem devices, as well as other devices, that are to be utilized to operate upon data that is represented in multiple dimensions either inaccurately provide approximations of Euclidean norms or are prohibitively complex and slow.
Accordingly, an improved manner by which to approximate Euclidean norms that is both accurate and computationally noncomplex is required.
It is in light of this background information related to digital communication systems, such as cellular communication systems, that the significant improvements of the present invention have evolved.